Flow graph

Wisemberg J and Kockarts G 1980 Negative ion chemistry in the terrestrial D region and signal flow graph theory J. Geophys. Res 85 4642-52... 

Signal-flow graphs are particularly useful in two respects. First, they make the process designer examine in considerable detail the dynamic structure and fimctioning of the process. Second, the nature of the interface between person and machine can be seen more clearly. The variables that are displayed in a system are, of course, available for study, but workers frequently respond to derivative functions of variables or "hidden" variables that must be deduced. Given that the process variables to be displayed will influence the worker s control strategy and that the number of deductions to be made will affect the mental workload involved, a process designer can select the type and amoimt of process information which will enhance performance of the task. 

Signal-flow graphs are useful in another sense they provide an objective representation of "how the system works" which can be used to evaluate the worker s subjective mental representation of the system. The influence modeling and assessment (IMAS) technique, which is described in subsequent sections, can also be used to elicit the worker s representation of the system. Both techniques, IMAS and SFG, can therefore be used for training personnel. 

Signal-flow graphs cannot explicitly identify the error potential for particular action steps. 

FIGURE 4.9. Block Diagram and Signal-Flow Graph for "Substance" Control System in Paper-Making (from Beishon, 1969). 

In the next two examples, we illustrate how state space models can handle a multiple-input multiple output (MIMO) problem. We ll show, with a simple example, how to translate information in a block diagram into a state space model. Some texts rely on signal-flow graphs, but we do not need them with simple systems. Moreover, we can handle complex problems easily with MATLAB. Go over MATLAB Session 4 before reading Example 4.7A. 

Let us take the trivial example in Fig. 3 to show the signal flow graph concept. In this example, the flowrates of streams 1,2, and 4 are considered measured. Performing a total mass balance around each unit and according to Eq. (3.1)... 

We have three equations, one for each unit. Solving these equations with respect to the variables fo, f, and f(, results in the associated signal flow graph shown in Figure 4. 

FIGURE 4 The signal flow graph for the system in Figure 3 (from Romagnoli and Stephanopoulos, 1980). 

The generic rank of (Aj A2) is 3 and the number of unmeasured process variables n = 4, so the system exhibits generic rank deficiency. The signal flow graph is given in Fig. 4. 

Figure 2.15 Signal flow graph of the M/S matrix (Reprinted from [Herre, 1995] 1995, courtesy of the author)...

C.S. Lorens, Flow Graphs for the Modelling and Analysis of Linear Systems, McGraw-Hill, Monographs in Modern Engineering Sciences, 1964. 

Mason, S. J. (1953). Feedback theory—some properties of signal flow graphs. Proc. I.R.E 41, 1144-1156. 

The fleet cash-flow graphs show the balance between investments in hydrogen vehicles (accounted negatively) and investment savings for conventional vehicles (accounted positively). 

The cash-flow graphs are scenario specific, that is, all the assumptions made about hydrogen costs, vehicle costs, penetration rates, fuel economy and so on are reflected in the resulting graphs. To obtain a smooth curve over the time period considered, polynomial curve fitting was applied between the time snapshots (T1-T4). 

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